Johannes Oude Groeniger
- Mathematical relativity;
- geometric PDE's;
- Hamiltonian dynamics.
My research, under supervision of Hans Ringström, is in the interplay of dynamics and geometry. This is especially present in Einstein's theory of general relativity, where both topics play a major role. Many interesting geometric and dynamical questions and problems arise naturally in this theory, concerning e.g. the influence of symmetry, long-term stability of solutions or the formation of singularities. For example, I have studied the nature of the initial singularity in so-called Bianchi VI0 spacetimes. These spacetimes contain a high degree of symmetry (homogeneity), and the precise symmetry has a large influence on the dynamics.
My current research project is on the U(1)-symmetric model in general relativity, which is a solution to Einstein's vacuum equations where the spatial topology is that of a circle bundle over a higher genus surface. Moncrief and Choquet-Bruhat showed the stability of this model under perturbations which are symmetric under the action of the circle. It is then of interest to understand what can happen as we consider perturbations in this direction as well: do we retain stability or do we find other interesting behaviour?
Lastly, as an aside, I am interested in the dynamics of resonant oscillators in Hamiltonian dynamics. Although the presence of resonance is non-generic, it leads to interesting dynamics and bifurcations, and I believe that -- as a transition stage -- it could potentially model the transfer of energy between different modes.
- On Bianchi type VI0 spacetimes with orthogonal perfect fluid matter arXiv:1908.02677.
In both 2020 and 2021 I am responsible for the exercise classes of Foundations of Analysis (SF 1677).